A Simple Explanation of the No-Rush Theorem (NRT) of the Theory of Entropicity (ToE)

The No-Rush Theorem (NRT) is a foundational principle within the Theory of Entropicity (ToE), a radical and provocative framework proposed by researcher John Onimisi Obidi in early (February) 2025. It posits that no physical process, interaction, event, or measurement can occur instantaneously, as all such phenomena require a finite, non-zero duration for the underlying entropic field—a dynamic, generative substrate of reality—to redistribute, reorganize, and synchronize states. In essence, the theorem enforces the idea that "nature cannot be rushed," meaning reality operates on an intrinsic "update schedule" dictated by entropy's finite rates of change, preventing any attempt to accelerate beyond these limits. This name reflects the theorem's core assertion: the universe's fundamental processes cannot be hurried or outpaced, as they are bound by entropy's inherent tempo.

Core Formulation and Definition

At its heart, NRT states that no process can reorganize or recalibrate the entropic field faster than the Entropic Speed Limit (ESL), which manifests in conventional physics as the speed of light (c ≈ 3 × 10^8 m/s). Unlike Einstein's special relativity, where c is an axiomatic constant derived from the invariance of light speed in all inertial frames, NRT reframes c as an emergent property—the maximum rate at which the entropic field can propagate energy, information, and causal influences. This "clock speed" of the entropic field ensures that causality is preserved: events must unfold over a minimum interaction time, as instantaneous changes would violate the field's dynamics.

Mathematically, the NRT itself is tied to broader constructs in ToE, such as the Obidi Action (a variational principle governing entropic dynamics) and the Master Entropic Equation (MEE), which describe how entropy evolves and constrains physical systems.

For instance, NRT underpins the concept of an "entropic cone," analogous to the light cone in relativity: events inside the cone are causally connected because they respect the ESL, while those outside are disconnected due to the field's finite update rate. In qualitative terms, if you imagine entropy as a fluid-like field that must "flow" to enable any change, NRT dictates that this flow cannot exceed a certain velocity, thus imposing delays on all interactions.

Relation to Entropy and Relativity

In ToE, entropy is elevated from a mere statistical measure of disorder (as in classical thermodynamics) to the primary, monistic field from which spacetime, matter, and forces emerge. NRT arises directly from this: since all physical reality stems from entropic rearrangements, no process can "outrun" the field's intrinsic pace. This connects deeply to relativity by deriving effects like time dilation, length contraction, and relativistic mass increase not from observer-dependent frames or spacetime curvature, but from entropic constraints. For example, as an object approaches the ESL, more entropic capacity is devoted to sustaining its motion, leaving less for internal processes (resulting in time slowing) or spatial integrity (causing contraction).

NRT also addresses quantum phenomena, such as decoherence in open systems, where entropy-driven interactions cause the loss of quantum coherence over finite times, supporting the theorem's non-instantaneous nature. It extends to general relativity corrections, like the Shapiro time delay (light bending near massive bodies) or Mercury's perihelion precession, which ToE reinterprets through an entropic coupling constant (η) rather than geometric curvature.

Implications for Physics

NRT has broad, radical implications:

Causality and the Arrow of Time: By mandating finite interaction times, it reinforces why causes precede effects and why time flows forward—entropy's irreversible redistribution prevents "rushing" backward or skipping steps.

Unification of Physics: It positions ToE as a potential bridge between thermodynamics, relativity, and quantum mechanics, deriving relativistic kinematics from first principles rather than postulates. For instance, it challenges models like the F-HUB theory (which prioritizes information over entropy) by arguing that entropy's dynamic enforcement of speed limits provides a more fundamental hierarchy: Entropy → Information → Mass → Motion → Spacetime.

Cosmological Insights: Through tools like the Generalized Entropic Expansion Equation (GEEE), NRT helps explain universe acceleration without invoking dark energy, attributing it to entropic flows instead.

Experimental Ties: Immediate [potential] evidence includes attosecond-scale limits on quantum entanglement formation, which suggest wave-function collapse isn't instantaneous, aligning with NRT's minimum times.

No one is longer left in doubt that the No-Rush Theorem (NRT) and the Theory of Entropicity (ToE) remain intriguing, intrusive and disruptive. They offer a philosophical shift, emphasizing entropy's primacy, and have been developed with  rigorous mathematical tools and insights.